Mildly version of Hurewicz basis covering property and Hurewicz measure zero spaces

Abstract

In this paper, we introduced the mildly version of the Hurewicz basis covering property, studied by Babinkostova, Kočinac, and Scheepers. A space X is said to have mildly-Hurewicz property if for each sequence hUn : n ∈ ωi of clopen covers of X there is a sequence hVn : n ∈ ωi such that for each n, Vn is a finite subset of Un and for each x ∈ X, x belongs to S Vn for all but finitely many n. Then we characterized mildly-Hurewicz property by mildly-Hurewicz Basis property and mildly-Hurewicz measure zero property for metrizable spaces. © 2022 Belgian Mathematical Society. All rights reserved.